MinT - Best Known (202−47, 202, s)-Nets in Base 2

Best Known (202−47, 202, s)-Nets in Base 2

(202−47, 202, 195)-Net over F₂ — Constructive and digital

Digital (155, 202, 195)-net over F₂, using

t-expansion [i] based on digital (154, 202, 195)-net over F₂, using
- 8 times m-reduction [i] based on digital (154, 210, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 70, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]

(202−47, 202, 341)-Net over F₂ — Digital

Digital (155, 202, 341)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−47, 202, 3995)-Net in Base 2 — Upper bound on s

There is no (155, 202, 3996)-net in base 2, because

1 times m-reduction [i] would yield (155, 201, 3996)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 229969 975552 161309 116411 141328 331727 280099 556488 309393 429298 > 2²⁰¹ [i]